Calculate the survey sample size needed for your confidence level, margin of error, expected proportion and population, plus invitations for your response rate.
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Results
Calculated
Required sample size
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Completed responses, finite-population adjusted
Unlimited-population size
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n0 = z²p(1−p)/e²
Confidence z-score
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Standard-normal critical value
Invitations to send
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After your response rate
Ready
Choose a confidence level and enter margin of error, proportion and population, then press Calculate.
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What this calculator finds
Sample size is how many completed responses a survey needs to estimate a percentage within a margin of error you choose, at a given confidence level. This calculator uses the Cochran formula for proportions, applies the finite-population correction when you provide the size of the group, and shows how many invitations to send once you allow for non-response.
Use it to plan customer surveys, polls, quality audits and any study that reports a share, such as the percent who agree or the percent defective.
The equations
n0 = z2 · p(1 − p) / e2, the sample for an unlimited population, where z is the confidence-level score, p the expected proportion and e the margin of error.
n = n0 / (1 + (n0 − 1) / N), the correction for a finite population of size N.
z is 1.645 for 90%, 1.96 for 95% and 2.576 for 99% confidence.
Invitations = n / response rate, always rounded up.
Worked example
A 95% confidence level, 5% margin of error, 50% expected proportion and a population of 10,000, the default inputs, with a 100% response rate.
n0 = 1.962 × 0.5 × 0.5 / 0.052 = 3.8416 × 0.25 / 0.0025 = 384.16, which rounds up to 385. With the finite-population correction, n = 384.16 / (1 + 383.16 / 10,000) = 384.16 / 1.038316 = 369.98, which rounds up to 370. The calculator shows 370 responses, with 385 as the unlimited-population figure. If only 40% of invitees respond, you would need to invite 370 / 0.40 = 925 people.
Common mistakes and how to read the result
Choosing a tiny margin of error. Halving the margin quadruples the sample.
Forgetting non-response. The main result is completed responses, not invitations.
Using it for subgroups. The margin applies to the whole sample; results for a subgroup are wider.
Assuming random sampling. The formula only holds for a simple random sample, not for convenience samples.
Frequently Asked Questions
Why use 50% when I do not know the proportion?
The product p(1 - p) is largest at 50%, so it gives the biggest sample size for any margin of error. If the true proportion is different, your margin will be tighter than planned, never wider.
Does population size matter?
Only when the sample is a sizable share of the population. For populations in the tens of thousands or more, the required sample barely changes, which is why national polls of about 1,000 people work.
Does the sample size include non-responses?
No. The main result is the number of completed responses you need. The last card divides by your response rate to show how many people to invite.
Is this suitable for means instead of proportions?
No. This is the Cochran formula for proportions. Sample sizes for a mean need the standard deviation, and comparisons between groups need a power calculation.
Sample Size Calculator is most useful when the inputs reflect the situation you are actually planning around, not a best-case estimate. Treat the result as a decision aid: it gives you a structured way to compare assumptions, spot outliers, and decide what to verify next. For Statistics work, the most important review lens is sample size, distribution assumptions, independence, uncertainty, and how the statistic will be interpreted.
Start with a baseline run using values you can defend. Then change one assumption at a time and watch which output moves the most. If one input dominates the result, spend your verification time there first. If several inputs have similar influence, use a conservative scenario and an optimistic scenario to create a practical range instead of relying on a single exact number.
Before acting on the result, verify the output with the raw data, summary statistics, and the assumptions behind the selected method. This is especially important when the calculator supports a purchase, project plan, performance target, or operational decision. The calculator can make the math consistent, but the quality of the conclusion still depends on current data, clear units, and assumptions that match your real constraints.
When the output looks surprising, slow down and inspect each input in order. A small change in one high-leverage field can move the final number more than several low-leverage fields combined. For Sample Size Calculator, that means you should first confirm the value with the greatest scale, then confirm the value with the greatest uncertainty, then rerun the calculator with conservative and optimistic assumptions. This sequence turns the calculator from a single answer into a practical decision range.
Review Checklist
Confirm every input uses the unit and time period requested by the calculator.
Run a low, expected, and high scenario so the answer has a useful range.
Check whether rounding or a missing decimal place changes the decision.
Update the calculation whenever the sample, hypothesis, confidence level, or decision threshold changes.